Four-port circulator with frequency conversion based on nondegenerate three waving mixing josephson devices

ABSTRACT

A technique relates to a superconducting device. A first mixing device has a first mixing port and a second mixing port. A second mixing device has another first mixing port and another second mixing port. The first and second mixing devices are superconducting nondegenerate three-wave mixing devices. The first mixing port and the another first mixing port are configured to couple to a first coupler. The second mixing port and the another second mixing port are configured to couple to a second coupler.

BACKGROUND

The present invention generally relates to superconducting devices. Morespecifically, the present invention relates to four-port circulatorswith frequency conversion based on nondegenerate three-wave mixingJosephson devices.

A circulator is a passive nonreciprocal three-port or four-port device,in which a microwave or radio frequency signal entering any port istransmitted to the next port in rotation (only). A port in this contextis a plane where an external waveguide or transmission line (such as amicrostrip line or a coaxial cable) connects to the device. For athree-port circulator, a signal applied to port 1 only comes out of port2. A signal applied to port 2 only comes out of port 3. A signal appliedto port 3 only comes out of port 1. Within a phase-factor, thescattering matrix for an ideal frequency-preserving three-portcirculator is

$S = {\begin{pmatrix}0 & 0 & 1 \\1 & 0 & 0 \\0 & 1 & 0\end{pmatrix}.}$

Circulators are used in superconducting circuits.

SUMMARY

Embodiments of the present invention are directed to a superconductingdevice. A non-limiting example of the superconducting device includes afirst mixing device having a first mixing port and a second mixing port,and a second mixing device having another first mixing port and anothersecond mixing port. The first and second mixing devices aresuperconducting nondegenerate three-wave mixing devices, where the firstmixing port and the another first mixing port are configured to coupleto a first coupler, and where the second mixing port and the anothersecond mixing port are configured to couple to a second coupler.

Embodiments of the present invention are directed to a method of forminga superconducting device. A non-limiting example of forming thesuperconducting device includes providing a first mixing device having afirst mixing port and a second mixing port, and providing a secondmixing device having another first mixing port and another second mixingport. The first and second mixing devices are superconductingnondegenerate three-wave mixing devices. The method includes couplingthe first mixing port and the another first mixing port to a firstcoupler, and coupling the second mixing port and the another secondmixing port to a second coupler.

Embodiments of the present invention are directed to a superconductingfour-port circulator. A non-limiting example of the superconductingfour-port circulator includes a first Josephson parametric device havinga first signal port and a second idler port, and a second Josephsonparametric device having another first signal port and another secondidler port. The first and second mixing devices are superconductingnondegenerate three-wave mixing devices, where the first signal port andthe another first signal port are configured to couple to a firstcoupler, and where the second idler port and the another second idlerport are configured to couple to a second coupler.

Embodiments of the present invention are directed to a method of forminga superconducting four-port circulator. A non-limiting example of themethod of forming the superconducting four-port circulator includesproviding a first Josephson parametric device having a first signal portand a second idler port, and providing a second Josephson parametricdevice having another first signal port and another second idler port.The first and second mixing devices are superconducting nondegeneratethree-wave mixing devices. Also, the method includes coupling the firstsignal port and the another first signal port to a first coupler, andcoupling the second idler port and the another second idler port to asecond coupler.

Embodiments of the present invention are directed to a method ofoperating a superconducting four-port circulator. A non-limiting exampleof the method of operating the superconducting four-port circulatorincludes receiving a signal at a port of a first coupler, where a firstJosephson parametric device and a second Josephson parametric device arecoupled in parallel to the first coupler and a second coupler. Themethod includes outputting the signal at a predefined port of the secondcoupler.

Additional technical features and benefits are realized through thetechniques of the present invention. Embodiments and aspects of theinvention are described in detail herein and are considered a part ofthe claimed subject matter. For a better understanding, refer to thedetailed description and to the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The specifics of the exclusive rights described herein are particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The foregoing and other features and advantages ofthe embodiments of the invention are apparent from the followingdetailed description taken in conjunction with the accompanying drawingsin which:

FIG. 1 depicts a schematic of a superconducting nondegenerate three-wavemixing device according to embodiments of the invention;

FIG. 2 depicts a signal flow graph of a superconducting nondegeneratethree-wave mixing device according to embodiments of the invention;

FIG. 3 depicts a schematic of a four-port circulator according toembodiments of the invention;

FIG. 4 depicts a symbol of a four-port circulator according toembodiments of the invention;

FIG. 5 depicts a schematic of a four-port circulator according toembodiments of the invention;

FIG. 6 depicts operation of a four-port circulator according toembodiments of the invention;

FIG. 7 depicts operation of a four-port circulator according toembodiments of the invention;

FIG. 8 depicts operation of a four-port circulator according toembodiments of the invention;

FIG. 9 depicts operation of a four-port circulator according toembodiments of the invention;

FIG. 10 depicts operation of a four-port circulator according toembodiments of the invention;

FIG. 11 depicts operation of a four-port circulator according toembodiments of the invention;

FIG. 12 depicts operation of a four-port circulator according toembodiments of the invention;

FIG. 13 depicts a flow chart of a method of forming a superconductingdevice according to embodiments of the invention;

FIG. 14 depicts a flow chart of a method of forming a superconductingfour-port circulator according to embodiments of the invention; and

FIG. 15 depicts a flow chart of a method of operating a superconductingfour-port circulator according to embodiments of the invention.

The diagrams depicted herein are illustrative. There can be manyvariations to the diagram or the operations described therein withoutdeparting from the spirit of the invention. For instance, the actionscan be performed in a differing order or actions can be added, deletedor modified. Also, the term “coupled” and variations thereof describeshaving a communications path between two elements and does not imply adirect connection between the elements with no interveningelements/connections between them. All of these variations areconsidered a part of the specification.

In the accompanying figures and following detailed description of thedisclosed embodiments, the various elements illustrated in the figuresare provided with two or three digit reference numbers. With minorexceptions, the leftmost digit(s) of each reference number correspond tothe figure in which its element is first illustrated.

DETAILED DESCRIPTION

For the sake of brevity, conventional techniques related tosemiconductor device and integrated circuit (IC) fabrication may or maynot be described in detail herein. Moreover, the various tasks andprocess steps described herein can be incorporated into a morecomprehensive procedure or process having additional steps orfunctionality not described in detail herein. In particular, varioussteps in the manufacture of semiconductor devices andsemiconductor-based ICs are well known and so, in the interest ofbrevity, many conventional steps will only be mentioned briefly hereinor will be omitted entirely without providing the well-known processdetails.

Turning now to an overview of technologies that are more specificallyrelevant to aspects of the invention, progress in solid-state quantuminformation processing has motivated the search for amplifiers andfrequency converters with quantum-limited performance in the microwavedomain. Depending on the gain applied to the quadratures of a singlespatial and temporal mode of the electromagnetic field, linearamplifiers can be classified into two categories which are phasesensitive and phase preserving, each having fundamentally differentnoise properties. Phase-sensitive amplifiers squeeze the input noise andsignal in one quadrature of the microwave field at the expense ofinflating the noise and signal in the other quadrature without addingnoise of their own to the processed signal. However, phase-sensitiveamplifiers are useful only in cases in which the quantum information isencoded in one quadrature of the microwave field. A phase-preservingamplifier on the other hand amplifies both quadratures of the inputnoise and signal at the expense of adding at least a noise equivalent toa half input photon at the signal frequency. Such an amplifier would beuseful in many quantum applications, including qubit readout. Onerealization of a nondegenerate intrinsically phase-preservingsuperconducting parametric amplifier is based on a Josephson ringmodulator. A Josephson ring modulator can include four Josephsonjunctions in a Wheatstone bridge configuration. The device symmetryenhances the purity of the amplification process, i.e., eliminates orminimizes certain undesired nonlinear processes, and also simplifiesboth its operation and its analysis.

Commercial cryogenic circulators are utilized in quantum applications.However, commercial cryogenic circulators are typically large in size,heavy in weight, and hard to thermalize. Additionally, commercialcryogenic circulators use ferrites which are difficult tofabricate/integrate on chip and incorporate magnets which can havenegative effects on superconducting circuits. In a standard 1 input 1output line setup, which connects 1 qubit-resonator and 1quantum-limited amplifier, such as the Josephson parametric converter(JPC), the state-of-the-art uses about two circulators and threeisolators.

Turning now to an overview of the aspects of the invention, one or moreembodiments of the invention address the above-described shortcomings ofthe prior art by providing superconducting nondegenerate three-wavemixing devices coupled together in parallel. More specifically, theabove-described aspects of the invention address the shortcomings of theprior art by providing a superconducting four-port circulator withfrequency conversion based at least in part on nondegenerate three-wavemixing Josephson devices. According to embodiments of the invention, thetechnical effects and benefits of the four-port circulator are that itcan be integrated on chip or into a printed circuit board (PCB), doesnot use ferrites, and does not require magnets (with large magneticfields). Also, the four-port circulator can be thermalized well, can bemade small/compact, and has lighter weight. Further, the direction ofisolation can be reversed in situ by negating the phase differencebetween the two pump tones feeding the two nondegenerate three-wavemixing devices. Further, embodiments allow for adding multiple four-portcirculators (i.e., scaling up) on the same chip with high density.

Turning now to a more detailed description of aspects of the presentinvention, FIG. 1 depicts a schematic of a superconducting nondegeneratethree-wave mixing device 130 according to embodiments of the invention.The superconducting nondegenerate three-wave mixing device 130 can be aJosephson parametric converter (as one example). The Josephsonparametric converter 130 includes a Josephson ring modulator (JRM) 105which is a nonlinear dispersive element based on Josephson tunneljunctions 102 that can perform three-wave mixing of microwave signals atthe quantum limit. The three microwave signals are generally referred toas the Signal microwave signal, Idler microwave signal, and Pumpmicrowave signal. The JRM 105 consists of four nominally identicalJosephson junctions 102 arranged in a Wheatstone bridge configuration.The JRM 105 can also include four nominally identical Josephson junction101 connected at the intersections of the Josephson junction 102. Insome implementations, the Josephson junctions 101 can be identical tothe Josephson junction 102. In other implementations, the Josephsonjunction 101 can be different from the Josephson junctions 102. In someimplementations, the JRM 105 may not include the Josephson junctions101.

In order to construct a nondegenerate parametric three-wave mixingdevice (the Josephson parametric converter 130), which is capable ofamplifying and/or mixing microwave signals at the quantum limit, the JRM105 is incorporated into two microwave resonators at a radio frequency(RF) current anti-node of the multiple of their eigenmodes. The JRM 105is driven by external flux, which is Φ_(ext). The external flux can beapplied using an on-chip flux line, using external magnetic coil, and/orusing a very small magnetic material integrated on-chip or in thepackage.

One of the microwave resonators is Signal (S) resonator 115A and theother is an Idler (I) resonator 115B. The device is nondegeneratebecause the Signal microwave signal and the Idler microwave signal areinput at separate ports. A coupling capacitor 110A connects theresonator 115A to a hybrid coupler while the coupling capacitor 110Bconnects the resonator 115B to a hybrid coupler. The hybrid couplers areoff-chip/on-chip broadband 180 degree hybrids. The Josephson parametricconverter 130 includes both the resonator 115A and resonator 115B, alongwith the JRM 105. The Signal (S) resonator 115A has a resonancefrequency f₁ (also referred to as f_(S)) and the Idler (I) resonator115B has a resonance frequency f₂ (also referred to as f₁). Embodimentsinclude the case in which the Josephson parametric converter 130 ishybrid-less, and this means that the Josephson parametric converter 130does not require hybrids for its operation, i.e., signal delivery to andfrom the device 130.

The performances (namely power gain G, dynamical bandwidth γ, andmaximum input power P_(max)) of the Josephson parametric converter 130are strongly dependent on the critical current I₀ of the Josephsonjunctions 102 of the JRM 105, the specific realization of theelectromagnetic environment (i.e., the microwave resonator 115A andmicrowave resonator 115B), the coupling between the JRM 105 and theresonators 115A and 115B, and the coupling between the resonators to thefeedlines. Feedlines are the transmission lines that connect theresonators 115A and 115B to the two hybrid couplers. The transmissionlines connecting the resonators 115A and 115B to the two hybrid couplerscan be microwave coaxial lines or waveguides. Although not shown, otherdevices can be connected to opposite end of the hybrid couplers.Examples of the other device can include attenuators, circulators,isolators, low-pass microwave filters, bandpass microwave filters,infrared filters, and qubit-cavity systems. FIG. 2 depicts a signal flowgraph of the superconducting nondegenerate three-wave mixing device 130operated in frequency conversion mode according to embodiments. Infrequency conversion mode, there is no photon gain. That is, thesuperconducting nondegenerate three-wave mixing device 130 is notoperated as an amplifier. FIG. 2 depicts the signal flow graph for thenondegenerate three-wave mixing device 130.

The Josephson parametric converter 130 satisfies the followingscattering matrix when operated in noiseless frequency conversion:

$\lbrack S\rbrack = {\begin{pmatrix}r & t \\t^{\prime} & r\end{pmatrix} = {\begin{pmatrix}{\cos \; \theta} & {{ie}^{i\; \phi_{P}}\sin \; \theta} \\{{ie}^{{- i}\; \phi_{P}}\sin \; \theta} & {\cos \; \theta}\end{pmatrix}.}}$

As we will recognized herein the phase of the pump φ_(p) will beutilized in accordance embodiments. Since the scattering matrix isunitary, the following relation holds

|r| ² +|t| ²=1,

where r is the reflection coefficient, t is the transmission parameter,and t′=t* (where t* is the conjugate of t). Unitary means that thedevice 130 preserves the energy and the coherence of the phase. The fullconversion working point of the superconducting nondegenerate three-wavemixing device 130 is

|r| ²=0, |t| ²=1.

At the full conversion working point, there is no reflection and thereis full transmission with frequency conversion.

In FIG. 2, the superconducting nondegenerate three-wave mixing device130 has 3 ports, which are the Signal port (S), the Idler port (I), andthe pump port (P). The superconducting nondegenerate three-wave mixingdevice 130 has transmission t from Idler port to Signal port andtransmission t′ from Signal port to Idler port. From Idler to Signalport, the Idler microwave signal enters the Idler port at frequency f₂,is down converted, and exits the Signal port at frequency f₁. FromSignal to Idler port, the Signal microwave signal enters the Signal portat frequency f₁, is up converted, and exits the Idler port at frequencyf₂. The pump microwave signal provides the energy for frequency upconversion and frequency down conversion. The pump frequency is f_(p),where

f _(P) =f ₁ −f _(S) =f ₂ −f ₁.

FIG. 3 depicts a schematic of an on-chip superconducting four-portcirculator 300 according to embodiments. FIG. 4 depicts a four-portcirculator symbol according to embodiments. The four-port circulator 300includes two superconducting nondegenerate three-wave mixing devices 130coupled together in parallel. The two superconducting nondegeneratethree-wave mixing devices are designated as superconductingnondegenerate three-wave mixing devices 130_1 and 130_2, which operatethe same as superconducting nondegenerate three-wave mixing devices 130discussed herein. For explanation purposes, the top path runs throughthe superconducting nondegenerate three-wave mixing devices 130_1, andthe bottom path runs through superconducting nondegenerate three-wavemixing devices 130_2. As understood by one skilled in the art, afour-port circulator has 4 ports: port 1, port 2, port 3, and port 4.Port 1 is designated as port 001, port 2 is designated as port 002, port3 is designated as port 003, and port 4 is designated as 004. In afour-port circulator, a microwave signal applied to port 1 only comesout of port 2. A microwave signal applied to port 2 only comes out ofport 3. A microwave signal applied to port 3 only comes out of port 4,and a microwave signal applied to port 4 only comes out of port 1.

The superconducting nondegenerate three-wave mixing devices 130_1 and130_2 are (nominally) identical. The superconducting nondegeneratethree-wave mixing devices 130_1 and 130_2 have respective ports 320_1and 320_2 (which can be Signal ports connected to Signal resonatorshaving the resonance frequency f₁). The superconducting nondegeneratethree-wave mixing devices 130_1 and 130_2 have respective ports 322_1and 322_2 (which can be Idler ports connected to Idler resonators havingthe resonance frequency f₂). The superconducting nondegeneratethree-wave mixing devices 130_1 and 130_2 have ports 324_1 and 324_2(which can be pump ports designed to receive the pump frequency f_(p)).The microwave pump signal at pump frequency f_(p) can be applied to thesignal resonator or the idler resonator through one of the Σ ports ofthe hybrids or directly (without hybrids) through a separate physicalport (as was demonstrated recently in several hybrid-less JPC circuits(in the state-of-the-art)). The microwave pump signal is applied at pumpports 324_1 and 324_2 with pump frequency f_(p) and phase φ_(p). For thesuperconducting nondegenerate three-wave mixing device 130_1, themicrowave pump signal is applied to port 324_1 at pump frequency f_(p)and phase φ_(p1). For the superconducting nondegenerate three-wavemixing device 130_2, the microwave pump signal is applied to port 324_2at pump frequency f_(p) and phase φ_(p2). The pump frequency f_(p) isf_(p)=|f₂−f₁| for the microwave pump signals input to both three-wavemixing devices 130_1 and 130_2 is the same, where f₂>f₁. The phaseφ_(p1)=φ₁ for the microwave pump signal applied at port 324_1. The phaseφ_(p2)=φ₁+90° for the microwave pump signal applied at port 324_2. Ascan be recognized, the microwave pump signal input into pump port 324_1for the superconducting nondegenerate three-wave mixing device 130_1 isout of phase with the microwave pump signal input into pump port 324_2for the superconducting nondegenerate three-wave mixing device 130_2 by90°. This 90° phase difference is utilized in conjunction with hybridcouplers 305A and 305B to form and operate the on-chip superconductingfour-port circulator 300 as a circulator according to embodiments.Additionally, the superconducting nondegenerate three-wave mixingdevices 130_1 and 130_2 are both operated at their full conversionworking point where reflection r is 0 and transmission |t is 1 andoperated in frequency conversion (i.e., not as an amplifier with photongain).

In FIG. 3, a 90° hybrid coupler 305A is connected to ports 320_1 and320_2. The 90° hybrid coupler 305A has two input ports designated asport 001 (i.e., port 1) and port 003 (i.e., port 3). A 180° hybridcoupler 305B is connected to ports 322_1 and 322_2. The 180° hybridcoupler 305B has two input ports designated as port 002 (i.e., port 2)and port 004 (i.e., port 4).

A 90° hybrid is a four-port microwave device which is reciprocal,matched, and ideally lossless. A 90° hybrid coupler is a specializedcoupler that has two output ports that are 90 degrees out of phase witheach other, splitting power equally between its two output ports. The90° hybrid splits an input signal into two equal amplitude outputs,where one output is in-phase with the input signal, while the otheroutput is 90° out-of-phase with the input signal.

A 180° hybrid is a four-port microwave device which is reciprocal,matched, and ideally lossless. The 180° hybrid splits an input signalinto two equal amplitude outputs. When fed from its sum port (Σ) (i.e.,0° port), the 180° hybrid provides two equal-amplitude in-phase outputsignals (which are also in-phase with the input signal), and when fedfrom its difference port (Δ) (i.e., 180° port), it provides twoequal-amplitude 180° out-of-phase output signals (one output in-phasewith the input signal, while the other is 180° out-of-phase with theinput signal). It should be noted that the 90° hybrids and 180° hybridsdo not need to be implemented using transmission-line circuits. The 90°hybrids and 180° hybrids can also be implemented using lumped elements(lumped capacitors and inductors). Examples of lumped capacitors includeplate capacitors, gap capacitors, interdigitated capacitors, etc.Examples of lumped inductors include, spirals and narrow, meanderingsuperconducting wires.

The operation mode of the devices 130_1 and 130_2 is unitary frequencyconversion mode (without photon gain) in which the applied pumpfrequency f_(P) satisfies the relation f_(P)=|f₁−f_(S)|.

Now providing more details of the operation of the four-port circulatordevice 300, the device 300 realizes an on-chip nondegenerate four-portcirculator. The device 300 transmits microwave signals entering thedevice ports in a certain (predefined) direction, and the signalsundergo unitary frequency conversion (up conversion/down conversion).For example, microwave signals entering port 1 (e.g., port 001) atfrequency f₁ are up converted to frequency f₂ and transmitted withoutloss or with low loss to port 2 (e.g., port 002). Microwave signalsentering port 2 (e.g., port 002) at frequency f₂ are down converted tofrequency f₁ and transmitted without loss or with low loss to port 3(e.g., port 003). Microwave signals entering port 3 (e.g., port 003) atfrequency f₁ are up converted to frequency f₂ and transmitted withoutloss or with low loss to port 4 (e.g., port 004). Microwave signalsentering port 4 (e.g., port 004) at frequency f₂ are down converted tofrequency f₁ and transmitted without loss or with low loss to port 1(e.g., port 001). The device 300 provides isolation in the oppositecirculation direction, i.e., port 1 is isolated from signals input onport 2, port 2 is isolated from signals input on port 3, port 3 isisolated from signals input on port 4, and port 4 is isolated fromsignals input on port 1. The (predefined) circulation direction is shownby the circular arrow, for example, in FIG. 4, while the oppositecirculation direction would be in the opposite direction of the circulararrow.

The device 300 consists of two stages of nondegenerate three-wave mixingJosephson devices 130_1 and 130_2, which can be Josephson parametricconverters. The two stages are connected in parallel, using two hybrids,i.e., 90° hybrid 305A and 180° hybrid. The two inputs of the 90° hybrid305A define ports 1 and 3 of the circulator 300, and the two outputs ofthe 90° hybrid 305A are connected to the signal ports 320_1 and 320_2 ofthe (JPC) stages. Similarly, the inputs of the 180° hybrid define ports2 and 4 of the circulator 300, and the two outputs of the 180° hybridare connected to the Idler ports 322_1 and 322_2 of the (JPC) stages.

By operating the nondegenerate three-wave mixing devices 130_1 and 130_2in noiseless frequency conversion mode (no photon gain) and settingtheir working point to full conversion, in which reflections off theports 320 and 322 are minimized and the transmissions (including upconversion/down conversion) to the other port (ports 320 and 322) aremaximized. The phase difference (phase φ_(p1)=φ₁ versus the phaseφ_(p2)=φ₁+90°) between the pump drives (via pump ports 324_1 and 324_2)feeding the two nondegenerate three-wave mixing Josephson devices 130_1and 130_2 introduces a non-reciprocal phase shift to the signalspropagating across the nondegenerate three-wave mixing Josephson devices130_1 and 130_2. It is noted that propagating across is illustrated asleft-to-right or right-to-left for explanation purposes, but one skilledit the under understands the orientation of the figures can be changed.During operation, the nondegenerate three-wave mixing Josephson device130_1 is configured to add a φ₁ phase shift to any signal received atport 320_1 (e.g., Signal port) and output at port 322_1 (Idler port). Inthe opposite direction, the nondegenerate three-wave mixing Josephsondevices 130_1 is configured to add a −φ₁ phase shift to any signalreceived at port 322_1 (Idler port) and output at port 320_1 (e.g.,Signal port). The addition of φ₁ or −φ₁ is related to the direction(which is left or right in the figures for explanation only) that thesignal is input into the nondegenerate three-wave mixing Josephsondevices 130_1. Because the pump signal (pump drive) received at port324_1 has the pump phase φ_(p1)=φ₁, the addition of φ₁ to the signalinput from port 320_1 output to port 322_1 occurs or the addition of −φ₁to the signal input from port 322_1 output to port 320_1 occurs.

A similar phase change happens in nondegenerate three-wave mixingJosephson device 130_1 according to its pump drive with phase φ₁+90°.During operation, the nondegenerate three-wave mixing Josephson device130_2 is configured to add a φ₁+90° phase shift to any signal receivedat port 320_2 (e.g., Signal port) and output at port 322_2 (Idler port).In the opposite direction, the nondegenerate three-wave mixing Josephsondevices 130_2 is configured to add a −φ₁−90° phase shift to any signalreceived at port 322_2 (Idler port) and output at port 320_2 (e.g.,Signal port). The addition of φ₁+90° or −φ₁−90° is related to thedirection (which is left or right in the figures for explanation only)that the signal is input into the nondegenerate three-wave mixingJosephson devices 130_2. Because the pump signal (pump drive) receivedat port 324_2 has the pump phase φ_(p1)=φ_(p1)+90°, the addition ofφ₁+90° to the signal input from port 320_2 output to port 322_2 occursor the addition of −φ₁−90° to the signal input from port 322_2 output toport 320_2 occurs.

The phase difference between the two pumps (i.e., the two microwave pumpsignals at frequency f_(p)) feeding the two stages is 90 degrees. Amicrowave pump is a device that generates microwave signals (also calledmicrowave tones). A microwave pump is connected to pump port 324_1 and aseparate microwave pump is connected to pump port 324_2. By reversingthis phase difference between the two microwave signals, the circulationdirection of the circulation can be reversed in-situ in oneimplementation.

In FIG. 3, each microwave pump drive is fed to its respective pump port324_1 and 324_2 via transmission lines. Instead of having two pumpdrives as shown in FIG. 3, one single pump drive can be fed to the wholedevice through a 90° hybrid coupler 505 as depicted in FIG. 5 accordingto embodiments. The 90° hybrid coupler 505 imposes the required phasedifference (i.e., 90° phase difference) between the pump drives injectedinto the two three-wave mixing stages. This assumes that the twonondegenerate three-wave mixing devices 130_1 and 130_2 are nominallyidentical. FIG. 5 shows that one port of the 90° hybrid coupler 505receives the microwave pump signal while the other input port of thehybrid is connected to a 50Ω termination.

The device operation of device 300 is based on wave interference betweentwo paths, in which one path passes through the first stage (e.g., toppath), and the other path that passes through the second stage (e.g.,bottom path). The wave interference is enabled via the hybrids 305_A and305_B, which act as beam-splitters. If the two split waves of an inputsignal of one port, passing through the two paths, add up constructively(in phase, i.e., peaks match) at a particular port, after being upconverted or down converted, the signal exits that port with almostunity transmission. Conversely, if the output waves destructivelyinterfere (have a phase difference of 180°) at a certain port, then thatport is isolated from the input port through which the signal entered.

For explanation purposes and not limitation, FIGS. 6-12 depict examplesof operating the four-port circulator 300 using wave interferenceaccording to embodiments.

FIG. 6 depicts operating the four-port circulator 300 when a microwavesignal at frequency f₁ is input to port 001 (e.g., port 1) of the 90°hybrid 305A to be output at port 002 (e.g., port 2) at frequency f₂according to embodiments. The microwave signal at frequency f₁ isreceived at port 001 of the 90° hybrid coupler 305A. The hybrid coupler305A is configured to split the power of the microwave signal receivedat port 001. The hybrid coupler 305A is configured to transmit the firstpart (i.e., ½) of the microwave signal (without a phase shift) to port320_1 of the superconducting nondegenerate three-wave mixing device130_1. Also, the 90° hybrid coupler 305A is configured to add a 90°phase shift to the second part (i.e., ½) of the microwave signal andtransmit the second part of the microwave signal to port 320_2 of thesuperconducting nondegenerate three-wave mixing devices 130_2.

The first part of the microwave signal (with no phase change) receivedat port 320_1 and the second part of microwave signal (with 90° phaseincrease) received at port 320_2 are both up converted from frequency f₁to frequency f₂ by their respective mixing devices 130_1 and 130_2.Additionally, the nondegenerate three-wave mixing Josephson device 130_1is configured to add a φ₁ phase shift to the first part of the microwavesignal having been received at port 320_1. Similarly, the nondegeneratethree-wave mixing Josephson device 130_2 is configured to add a φ₁+90°phase shift to the 90° phase of the second part of microwave signalhaving been received at port 320_2, resulting in φ₁+180°.

The up converted first part of the microwave signal at frequency f₂ withphase φ₁ is transmitted from mixing device 130_1 to the hybrid coupler305B, and the up converted second part of microwave signal at frequencyf₂ with phase φ₁+180° is transmitted from mixing device 130_2 to the180° hybrid coupler 305B. The 180° hybrid coupler 305B is configured totransmit the up converted first part of microwave signal at frequency f₂with phase φ₁ to port 002, which means the 180° hybrid coupler 305B addsno phase. After receiving the up converted second part of microwavesignal at frequency f₂ with phase φ₁+180°, the 180° hybrid coupler 305Bis configured to add 180° phase to the phase φ₁+180°, resulting in phaseφ₁+360°, and transmit the up converted second part of microwave signalat frequency f₂ with phase φ₁+360° to port 002. Constructiveinterference occurs at port 002 of the microwave signals transmittedfrom mixing devices 130_1 and 130_2. At output port 002 of the 180°hybrid coupler 305B, the phase of the first part of microwave signalfrom the top path has phase φ₁ and the phase from the second part ofmicrowave signal from the bottom path has phase φ₁+360°. Therefore, thetwo microwave signals (having been received from mixing devices 130_1and 130_2) add constructively via hybrid coupler 305B to be output atport 002, such that the microwave signal at frequency f₁ is input toport 001 of the 90° hybrid 305A and output at port 002 (e.g., port 2) of180° hybrid 305B at frequency f₂. However, with respect to port 004 ofthe 180° hybrid 305B, the first part and second part of the microwavesignals (having been received from mixing devices 130_1 and 130_2) adddestructively via hybrid coupler 305B and no microwave signal is outputfrom port 004.

FIG. 7 depicts operating the four-port circulator 300 when a microwavesignal at frequency f₂ is input to port 002 (e.g., port 2) of the 180°hybrid 305B to be output at port 001 (e.g., port 1) at frequency f₁according to embodiments. However, destructive interference occurs inthis example. The microwave signal at frequency f₂ is received at port002 of the 180° hybrid coupler 305B. The hybrid coupler 305B isconfigured to split the power of the microwave signal received at port002. The hybrid coupler 305B is configured to transmit the first part(i.e., ½) of the microwave signal (without a phase shift) to port 322_1of the superconducting nondegenerate three-wave mixing device 130_1.Also, the 180° hybrid coupler 305A is configured to add a 180° phaseshift to the second part (i.e., ½) of the microwave signal and transmitthe second part of the microwave signal to port 322_2 of thesuperconducting nondegenerate three-wave mixing devices 130_2.

The first part of the microwave signal (with no phase change) receivedat port 322_1 and the second part of microwave signal with 180° phasereceived at port 322_2 are both down converted from frequency f₂ tofrequency f₁ by their respective mixing devices 130_1 and 130_2.Additionally, the nondegenerate three-wave mixing Josephson device 130_1is configured to add a −φ₁ phase shift to the first part of themicrowave signal having been received at port 322_1. Similarly, thenondegenerate three-wave mixing Josephson device 130_2 is configured toadd a −φ₁−90° phase shift to the 180° phase of the second part ofmicrowave signal having been received at port 322_2, resulting in−φ₁+−90°.

The down converted first part of the microwave signal at frequency f₁with phase φ₁ is transmitted from mixing device 130_1 to the 90° hybridcoupler 305A, and the down converted second part of microwave signal atfrequency f₁ with phase −φ₁+90° is transmitted from mixing device 130_2to the 90° hybrid coupler 305A. The 90° hybrid coupler 305A isconfigured to transmit the down converted first part of microwave signalat frequency f₁ with phase −φ₁ to port 001, which means the 90° hybridcoupler 305A adds no phase. After receiving the down converted secondpart of microwave signal at frequency f₁ with phase −φ₁+90°, the 90°hybrid coupler 305A is configured to add 90° phase to the phase −φ₁+90°,resulting in phase −φ₁+180°, and transmit the up converted second partof microwave signal at frequency f₂ with phase −φ₁+180° to port 001.Destructive interference occurs at port 001 of the microwave signalstransmitted from mixing devices 130_1 and 130_2. At output port 001 ofthe 90° hybrid coupler 305A, the phase of the first part of microwavesignal from the top path has phase −φ₁ and the phase from the secondpart of microwave signal from the bottom path has phase −φ₁+180°.Therefore, the two microwave signals (having been received from mixingdevices 130_1 and 130_2) add destructively via hybrid coupler 305A andthere is no microwave signal output at port 001. However, with respectto port 003 of the 90° hybrid 305A, the first part and second part ofthe microwave signals (having been received from mixing devices 130_1and 130_2) add constructively via hybrid coupler 305A and the microwavesignal is output from port 003, as depicted in FIG. 8.

FIG. 8 depicts operating the four-port circulator 300 when a microwavesignal at frequency f₂ is input to port 002 (e.g., port 2) of the 180°hybrid 305B to be output at port 003 (e.g., port 3) at frequency f₁according to embodiments. The microwave signal at frequency f₂ isreceived at port 002 of the 180° hybrid coupler 305B. The hybrid coupler305B is configured to split the power of the microwave signal receivedat port 002. The hybrid coupler 305B is configured to transmit the firstpart (i.e., ½) of the microwave signal (without a phase shift) to port322_1 of the superconducting nondegenerate three-wave mixing device130_1. Also, the 180° hybrid coupler 305A is configured to add a 180°phase shift to the second part (i.e., ½) of the microwave signal andtransmit the second part of the microwave signal to port 322_2 of thesuperconducting nondegenerate three-wave mixing devices 130_2.

The first part of the microwave signal (with no phase change) receivedat port 322_1 and the second part of microwave signal with 180° phasereceived at port 322_2 are both down converted from frequency f₂ tofrequency f₁ by their respective mixing devices 130_1 and 130_2.Additionally, the nondegenerate three-wave mixing Josephson device 130_1is configured to add a −φ₁ phase shift to the first part of themicrowave signal having been received at port 322_1. Similarly, thenondegenerate three-wave mixing Josephson device 130_2 is configured toadd a −φ₁−90° phase shift to the 180° phase of the second part ofmicrowave signal having been received at port 322_2, resulting in phase−φ₁+90°.

The down converted first part of the microwave signal at frequency f₁with phase φ₁ is transmitted from mixing device 130_1 to the 90° hybridcoupler 305A, and the down converted second part of microwave signal atfrequency f₁ with phase −φ₁+90° is transmitted from mixing device 130_2to the 90° hybrid coupler 305A. After receiving the down converted firstpart of microwave signal at frequency f₁ with phase −φ₁, the 90° hybridcoupler 305A is configured to add 90° phase to the phase −φ₁, resultingin phase −φ₁+90°, and transmit the down converted first part ofmicrowave signal at frequency f₁ with phase −φ₁+90° to port 003. The 90°hybrid coupler 305A is configured to transmit the down converted secondpart of microwave signal at frequency f₁ with phase −φ₁+90° to port 003,which means the 90° hybrid coupler 305A adds no phase. Constructiveinterference occurs at port 003 for the microwave signals transmittedfrom mixing devices 130_1 and 130_2. At output port 003 of the 90°hybrid coupler 305A, the phase of the first part of microwave signalfrom the top path has phase −φ₁+90° and the phase of the second part ofmicrowave signal from the bottom path has phase −φ₁+90°. Therefore, thetwo microwave signals (having been received from mixing devices 130_1and 130_2) add constructively via hybrid coupler 305A and the combinedmicrowave signal is output at port 003. The destructive interference wasdepicted in FIG. 7 at port 001.

FIG. 9 depicts operating the four-port circulator 300 when a microwavesignal at frequency f₁ is input to port 003 (e.g., port 3) of the 90°hybrid 305A to be output at port 002 (e.g., port 2) at frequency f₂according to embodiments. Destructive interference occurs in thisscenario. The microwave signal at frequency f₁ is received at port 003of the 90° hybrid coupler 305A. The hybrid coupler 305A is configured tosplit the power of the microwave signal received at port 003. Also, the90° hybrid coupler 305A is configured to add a 90° phase shift to thefirst part (i.e., ½) of the microwave signal and transmit the first partof the microwave signal to port 320_1 of the superconductingnondegenerate three-wave mixing devices 130_1. The hybrid coupler 305Ais configured to transmit the second part (i.e., ½) of the microwavesignal (without a phase shift) to port 320_2 of the superconductingnondegenerate three-wave mixing device 130_2.

The first part of the microwave signal (with 90° phase increase)received at port 320_1 and the second part of microwave signal (with nophase change) received at port 320_2 are both up converted fromfrequency f₁ to frequency f₂ by their respective mixing devices 130_1and 130_2. Additionally, the nondegenerate three-wave mixing Josephsondevice 130_1 is configured to add a φ₁ phase shift to the first part ofthe microwave signal having been received at port 320_1, resulting inφ₁+90°. Similarly, the nondegenerate three-wave mixing Josephson device130_2 is configured to add a φ₁+90° phase shift to the second part ofmicrowave signal having been received at port 320_2, resulting in phaseφ₁+90°.

The up converted first part of the microwave signal at frequency f₂ withphase φ₁+90° is transmitted from mixing device 130_1 to the hybridcoupler 305B, and the up converted second part of microwave signal atfrequency f₂ with phase φ₁+90° is transmitted from mixing device 130_2to the 180° hybrid coupler 305B. The 180° hybrid coupler 305B isconfigured to transmit the up converted first part of microwave signalat frequency f₂ with phase φ₁+90° to port 002, which means the 180°hybrid coupler 305B adds no phase. After receiving the up convertedsecond part of microwave signal at frequency f₂ with phase φ₁+90°, the180° hybrid coupler 305B is configured to add 180° phase to the phaseφ₁+180°, resulting in phase φ₁+270°, and transmit the up convertedsecond part of microwave signal at frequency f₂ with phase φ₁+270° toport 002. Destructive interference occurs at port 002 of the microwavesignals transmitted from mixing devices 130_1 and 130_2. At output port002 of the 180° hybrid coupler 305B, the phase of the first part ofmicrowave signal from the top path has phase φ₁+90° and the phase fromthe second part of microwave signal from the bottom path has phaseφ₁+270°. Therefore, the two microwave signals (having been received frommixing devices 130_1 and 130_2) add destructively via hybrid coupler305B, and no microwave signal is output at port 002. However, withrespect to port 004 of the 180° hybrid 305B, the first part and secondpart of the microwave signals (having been received from mixing devices130_1 and 130_2) add constructively via hybrid coupler 305B and acombined microwave signal is output from port 004, as depicted in FIG.10.

FIG. 10 depicts operating the four-port circulator 300 when a microwavesignal at frequency f₁ is input to port 003 (e.g., port 3) of the 90°hybrid 305A to be output at port 004 (e.g., port 4) at frequency f₂according to embodiments. The microwave signal at frequency f₁ isreceived at port 003 of the 90° hybrid coupler 305A. The hybrid coupler305A is configured to split the power of the microwave signal receivedat port 003. Also, the 90° hybrid coupler 305A is configured to add a90° phase shift to the first part (i.e., ½) of the microwave signal andtransmit the first part of the microwave signal to port 320_1 of thesuperconducting nondegenerate three-wave mixing devices 130_1. Thehybrid coupler 305A is configured to transmit the second part (i.e., ½)of the microwave signal (without a phase shift) to port 320_2 of thesuperconducting nondegenerate three-wave mixing device 130_2.

The first part of the microwave signal (with 90° phase increase)received at port 320_1 and the second part of microwave signal (with nophase change) received at port 320_2 are both up converted fromfrequency f₁ to frequency f₂ by their respective mixing devices 130_1and 130_2. Additionally, the nondegenerate three-wave mixing Josephsondevice 130_1 is configured to add a φ₁ phase shift to the first part ofthe microwave signal having been received at port 320_1, resulting inphase φ₁+90°. Similarly, the nondegenerate three-wave mixing Josephsondevice 130_2 is configured to add a φ₁+90° phase shift to the secondpart of microwave signal having been received at port 320_2, resultingin phase φ₁+90°.

The up converted first part of the microwave signal at frequency f₂ withphase φ₁+90° is transmitted from mixing device 130_1 to the hybridcoupler 305B, and the up converted second part of microwave signal atfrequency f₂ with phase φ₁+90° is transmitted from mixing device 130_2to the 180° hybrid coupler 305B. After receiving up converted first partof the microwave signal at frequency f₂ with phase φ₁+90°, the 180°hybrid coupler 305B is configured add 0° phase (no phase shift) to phaseφ₁+90° and to transmit the up converted first part of microwave signalat frequency f₂ with phase φ₁+90° to port 004, which means the 180°hybrid coupler 305B adds no phase. After receiving the up convertedsecond part of microwave signal at frequency f₂ with phase φ₁+90°, the180° hybrid coupler 305B is configured to transmit the up convertedsecond part of microwave signal at frequency f₂ with phase φ₁+90° toport 004. Constructive interference occurs at port 004 for the microwavesignals transmitted from mixing devices 130_1 and 130_2. At output port004 of the 180° hybrid coupler 305B, the phase of the first part ofmicrowave signal from the top path has phase φ₁+90° and the phase of thesecond part of microwave signal from the bottom path has phase φ₁+90°.Therefore, the two microwave signals (having been received from mixingdevices 130_1 and 130_2) add constructively via hybrid coupler 305B, anda combined microwave signal is output at port 004. However, with respectto port 002 of the 180° hybrid 305B, the first part and second part ofthe microwave signals (having been received from mixing devices 130_1and 130_2) add destructively via hybrid coupler 305B and no microwavesignal is output from port 002, as depicted in FIG. 9.

FIG. 11 depicts operating the four-port circulator 300 when a microwavesignal at frequency f₂ is input to port 004 (e.g., port 4) of the 180°hybrid 305B to be output at port 003 (e.g., port 3) at frequency f₁according to embodiments. This scenario depicts destructiveinterference. The microwave signal at frequency f₂ is received at port004 of the 180° hybrid coupler 305B. The hybrid coupler 305B isconfigured to split the power of the microwave signal received at port004. The 180° hybrid coupler 305A is configured to add a 0° phase shiftto the first part (i.e., ½) of the microwave signal and transmit thefirst part of the microwave signal to port 322_1 of the superconductingnondegenerate three-wave mixing devices 130_1. The hybrid coupler 305Bis configured to transmit the second part (i.e., ½) of the microwavesignal (without a phase shift) to port 322_2 of the superconductingnondegenerate three-wave mixing device 130_2.

The first part of the microwave signal with 0° phase received at port322_1 and the second part of microwave signal with no phase (i.e., 0°)change received at port 322_2 are both down converted from frequency f₂to frequency f₁ by their respective mixing devices 130_1 and 130_2.Additionally, the nondegenerate three-wave mixing Josephson device 130_1is configured to add a −φ₁ phase shift to 0° phase of the first part ofthe microwave signal having been received at port 322_1, resulting inphase −φ₁. Similarly, the nondegenerate three-wave mixing Josephsondevice 130_2 is configured to add a −φ₁−90° phase shift to the 0° phaseof the second part of microwave signal having been received at port322_2, resulting in phase −φ₁−90°.

The down converted first part of the microwave signal at frequency f₁with phase −φ₁ is transmitted from mixing device 130_1 to the 90° hybridcoupler 305A, and the down converted second part of microwave signal atfrequency f₁ with phase −φ₁−90° is transmitted from mixing device 130_2to the 90° hybrid coupler 305A. After receiving the down converted firstpart of microwave signal at frequency f₁ with phase −φ₁, the 90° hybridcoupler 305A is configured to add 90° phase to the phase −φ₁, resultingin phase −φ₁+90°, and transmit the up converted first part of microwavesignal at frequency f₂ with phase −φ₁+90° to port 003. The 90° hybridcoupler 305A is configured to transmit the down converted second part ofmicrowave signal at frequency f₁ with phase −φ₁−90° to port 003, whichmeans the 90° hybrid coupler 305A adds no phase. Destructiveinterference occurs at port 003 for the microwave signals transmittedfrom mixing devices 130_1 and 130_2. Therefore, the two microwavesignals (having been received from mixing devices 130_1 and 130_2) adddestructively via hybrid coupler 305A and no microwave signal is outputat port 003. The constructive interference occurs at port 001, asdepicted in FIG. 12.

FIG. 12 depicts operating the four-port circulator 300 when a microwavesignal at frequency f₂ is input to port 004 (e.g., port 4) of the 180°hybrid 305B to be output at port 001 (e.g., port 1) at frequency f₁according to embodiments. The microwave signal at frequency f₂ isreceived at port 004 of the 180° hybrid coupler 305B. The hybrid coupler305B is configured to split the power of the microwave signal receivedat port 004. The 180° hybrid coupler 305A is configured to add a 0°phase shift to the first part (i.e., ½) of the microwave signal andtransmit the first part of the microwave signal to port 322_1 of thesuperconducting nondegenerate three-wave mixing devices 130_1. Thehybrid coupler 305B is configured to transmit the second part (i.e., ½)of the microwave signal (without a phase shift) to port 322_2 of thesuperconducting nondegenerate three-wave mixing device 130_2.

The first part of the microwave signal with 0° phase received at port322_1 and the second part of microwave signal with no phase change(i.e., 0°) received at port 322_2 are both down converted from frequencyf₂ to frequency f₁ by their respective mixing devices 130_1 and 130_2.Additionally, the nondegenerate three-wave mixing Josephson device 130_1is configured to add a −φ₁ phase shift to the 0° phase of the first partof the microwave signal having been received at port 322_1, resulting inphase −φ₁. Similarly, the nondegenerate three-wave mixing Josephsondevice 130_2 is configured to add a −φ₁−90° phase shift to the 0° phaseof the second part of microwave signal having been received at port322_2, resulting in phase −φ₁−90°.

The down converted first part of the microwave signal at frequency f₁with phase −φ₁ is transmitted from mixing device 130_1 to the 90° hybridcoupler 305A, and the down converted second part of microwave signal atfrequency f₁ with phase −φ₁−90° is transmitted from mixing device 130_2to the 90° hybrid coupler 305A. The 90° hybrid coupler 305A isconfigured to transmit the down converted first part of microwave signalat frequency f₁ with phase −φ₁ to port 001, which means the 90° hybridcoupler 305A adds no phase. After receiving the down converted secondpart of microwave signal at frequency f₁ with phase −φ₁−90°, the 90°hybrid coupler 305A is configured to add 90° phase to the phase −φ₁−90°,resulting in phase −φ₁, and transmit the up converted first part ofmicrowave signal at frequency f₂ with phase −φ₁ to port 001.

Constructive interference occurs at port 001 for the microwave signalstransmitted from mixing devices 130_1 and 130_2. Therefore, the twomicrowave signals (having been received from mixing devices 130_1 and130_2) add constructively via hybrid coupler 305A and a combinedmicrowave signal is output at port 001. The destructive interferenceoccurs at port 003, as depicted in FIG. 11.

From the scenarios provided above, it should be appreciated that when acombined microwave signal is output from one output port (viaconstructive interference) of hybrid coupler 305A destructiveinterference occurs at the other output port of hybrid coupler 305A suchthat no signal is output. Likewise, it should be appreciated that when acombined microwave signal is output from one output port (viaconstructive interference) of hybrid coupler 305B destructiveinterference occurs at the other output port of hybrid coupler 305B suchthat no signal is output.

FIG. 13 depicts a flow chart 1300 of a method of forming asuperconducting device 300 according to embodiments. At block 1302, afirst mixing device 130_1 having a first mixing port 320_1 and a secondmixing port 322_1 is provided. At block 1304, a second mixing device130_2 having another first mixing port 320_2 and another second mixingport 322_2 is provided. The first and second mixing devices 130_1, 130_2are superconducting nondegenerate three-wave mixing devices.

At block 1306, the first mixing port 320_1 and the another first mixingport 320_2 are coupled to a first coupler 305A. At block 1308, thesecond mixing port 322_1 and the another second mixing port 322_2 arecoupled to a second coupler 305B.

The first mixing device 130_1 and the second mixing device 130_1 arecoupled together in parallel. The first mixing port 320_1 of the firstmixing device 130_1 and the another first mixing port 320_2 of thesecond mixing device 130_2 are configured to have a first functionality.The first functionality can be respectively operating as Signalresonators 115A, receiving signals at frequency f₁, and outputtingsignals at frequency f₁.

The second mixing port 322_1 of the first mixing device 130_1 and theanother second mixing port 322_2 of the second mixing device 130_2 areconfigured to have a second functionality. The second functionality canbe respectively operating as Idler resonators 115B, receiving signals atfrequency f₂, and outputting signals at frequency f₂.

The first mixing device 130_1 has a third mixing port 324_1 and thesecond mixing device 130_2 has another third mixing port 324_2. Thethird mixing port 324_1 of the first mixing device 130_1 and the anotherthird mixing port 324_2 of the second mixing device 130_2 are configuredto have a third functionality. The third functionality can berespectively receiving pump signals for operating the device inconversion mode (without photon gain) in which the applied pumpfrequency fp satisfies the relation f_(P)=|f_(I)−f_(S)|or|f₂−f₁|, wherepump signal input to port 324_1 has phase φ_(p1)=φ₁ and the pump signalinput to port 324_2 has phase φ_(p2)=φ₁+90°.

The first mixing device 130_1 and the second mixing device 130_2 areconfigured to receive a signal from the first coupler 305A. The firstmixing device 130_1 and the second mixing device 130_2 are configured tooutput the signal to the second coupler 305B, the signal having beenconverted by the first mixing device 130_1 and the second mixing device130_2 such that the second coupler 305B is configured to output thesignal via one port.

The first mixing device 130_1 and the second mixing device 130_2 areconfigured to receive a signal from the second coupler 305A. The firstmixing device 130_1 and the second mixing device 130_2 are configured tooutput the signal to the first coupler 305A, the signal having beenconverted by the first mixing device 130_1 and the second mixing device130_2 such that the first coupler 305A is configured to output thesignal via one port.

The first coupler and the second coupler are 90 degree hybrid couplers,the first coupler is a 90 degree hybrid coupler and the second coupleris a 180 degree hybrid coupler, or the first coupler is a 180 degreehybrid coupler and the second coupler is a 90 degree hybrid coupler.

FIG. 14 depicts a flow chart 1400 of a method of forming asuperconducting four-port circulator 300 according to embodiments. Atblock 1402, a first Josephson parametric device 130_1 having a firstsignal port 320_1 and a second idler port 322_1 is provided. At block1404, a second Josephson parametric device 130_1 having another firstsignal port 320_2 and another second idler port 322_2, the first andsecond mixing devices 130_1, 130_2 being superconducting nondegeneratethree-wave mixing devices.

At block 1406, the first signal port 320_1 and the another first signalport 320_2 are coupled to a first coupler 305A. At block 1408, thesecond idler port 322_1 and the another second idler port 322_2 arecoupled to a second coupler 305B.

FIG. 15 is a flow chart 1500 of a method of operating a superconductingfour-port circulator 300 according to embodiments. At block 1502, asignal is received at a port of a first coupler 305A, wherein a firstJosephson parametric device 130_1 and a second Josephson parametricdevice 130_2 are coupled in parallel to the first coupler 305A and asecond coupler 305B. At block 1504, the signal is output at a predefinedport of the second coupler 305B (according to the predefined circulationpattern of the circulator 400).

The circuit elements of the circuits 330, 130_1, 130_2 can be made ofsuperconducting material. The respective resonators andtransmission/feed/pump lines are made of superconducting materials. Thehybrid couplers can be made of superconducting materials. Examples ofsuperconducting materials (at low temperatures, such as about 10-100millikelvin (mK), or about 4 K) include niobium, aluminum, tantalum,etc. For example, the Josephson junctions are made of superconductingmaterial, and their tunnel junctions can be made of a thin tunnelbarrier, such as an oxide. The capacitors can be made of superconductingmaterial separated by dielectric material with very low-loss. Thetransmission lines (i.e., wires) connecting the various elements aremade of a superconducting material.

Various embodiments of the present invention are described herein withreference to the related drawings. Alternative embodiments can bedevised without departing from the scope of this invention. Althoughvarious connections and positional relationships (e.g., over, below,adjacent, etc.) are set forth between elements in the followingdescription and in the drawings, persons skilled in the art willrecognize that many of the positional relationships described herein areorientation-independent when the described functionality is maintainedeven though the orientation is changed. These connections and/orpositional relationships, unless specified otherwise, can be direct orindirect, and the present invention is not intended to be limiting inthis respect. Accordingly, a coupling of entities can refer to either adirect or an indirect coupling, and a positional relationship betweenentities can be a direct or indirect positional relationship. As anexample of an indirect positional relationship, references in thepresent description to forming layer “A” over layer “B” includesituations in which one or more intermediate layers (e.g., layer “C”) isbetween layer “A” and layer “B” as long as the relevant characteristicsand functionalities of layer “A” and layer “B” are not substantiallychanged by the intermediate layer(s).

The following definitions and abbreviations are to be used for theinterpretation of the claims and the specification. As used herein, theterms “comprises,” “comprising,” “includes,” “including,” “has,”“having,” “contains” or “containing,” or any other variation thereof,are intended to cover a non-exclusive inclusion. For example, acomposition, a mixture, process, method, article, or apparatus thatcomprises a list of elements is not necessarily limited to only thoseelements but can include other elements not expressly listed or inherentto such composition, mixture, process, method, article, or apparatus.

Additionally, the term “exemplary” is used herein to mean “serving as anexample, instance or illustration.” Any embodiment or design describedherein as “exemplary” is not necessarily to be construed as preferred oradvantageous over other embodiments or designs. The terms “at least one”and “one or more” are understood to include any integer number greaterthan or equal to one, i.e. one, two, three, four, etc. The terms “aplurality” are understood to include any integer number greater than orequal to two, i.e. two, three, four, five, etc. The term “connection”can include an indirect “connection” and a direct “connection.”

References in the specification to “one embodiment,” “an embodiment,”“an example embodiment,” etc., indicate that the embodiment describedcan include a particular feature, structure, or characteristic, butevery embodiment may or may not include the particular feature,structure, or characteristic. Moreover, such phrases are not necessarilyreferring to the same embodiment. Further, when a particular feature,structure, or characteristic is described in connection with anembodiment, it is submitted that it is within the knowledge of oneskilled in the art to affect such feature, structure, or characteristicin connection with other embodiments whether or not explicitlydescribed.

For purposes of the description hereinafter, the terms “upper,” “lower,”“right,” “left,” “vertical,” “horizontal,” “top,” “bottom,” andderivatives thereof shall relate to the described structures andmethods, as oriented in the drawing figures. The terms “overlying,”“atop,” “on top,” “positioned on” or “positioned atop” mean that a firstelement, such as a first structure, is present on a second element, suchas a second structure, wherein intervening elements such as an interfacestructure can be present between the first element and the secondelement. The term “direct contact” means that a first element, such as afirst structure, and a second element, such as a second structure, areconnected without any intermediary conducting, insulating orsemiconductor layers at the interface of the two elements.

The phrase “selective to,” such as, for example, “a first elementselective to a second element,” means that the first element can beetched and the second element can act as an etch stop.

The terms “about,” “substantially,” “approximately,” and variationsthereof, are intended to include the degree of error associated withmeasurement of the particular quantity based upon the equipmentavailable at the time of filing the application. For example, “about”can include a range of ±8% or 5%, or 2% of a given value.

As previously noted herein, for the sake of brevity, conventionaltechniques related to superconducting device and integrated circuit (IC)fabrication may or may not be described in detail herein. By way ofbackground, however, a more general description of the superconductingdevice fabrication processes that can be utilized in implementing one ormore embodiments of the present invention will now be provided. Althoughspecific fabrication operations used in implementing one or moreembodiments of the present invention can be individually known, thedescribed combination of operations and/or resulting structures of thepresent invention are unique. Thus, the unique combination of theoperations described in connection with the fabrication of asemiconductor device according to the present invention utilize avariety of individually known physical and chemical processes performedon a superconductor over a dielectric (e.g., silicon) substrate, some ofwhich are described in the immediately following paragraphs.

In general, the various processes used to form a micro-chip that will bepackaged into an IC fall into general categories, including, filmdeposition, removal/etching, and patterning/lithography. Deposition isany process that grows, coats, or otherwise transfers a material ontothe wafer. Available technologies include physical vapor deposition(PVD), chemical vapor deposition (CVD), electrochemical deposition(ECD), molecular beam epitaxy (MBE) and more recently, atomic layerdeposition (ALD) among others. Removal/etching is any process thatremoves material from the wafer. Examples include etch processes (eitherwet or dry), and chemical-mechanical planarization (CMP), and the like.Films of both conductors (e.g., poly-silicon, aluminum, copper, etc.)and insulators (e.g., various forms of silicon dioxide, silicon nitride,etc.) are used to connect and isolate components. Lithography is theformation of three-dimensional relief images or patterns on thesemiconductor substrate for subsequent transfer of the pattern to thesubstrate. In lithography, the patterns are formed by a light sensitivepolymer called a photo-resist. To build the complex structures of acircuit, lithography and etch pattern transfer steps are repeatedmultiple times. Each pattern being printed on the wafer is aligned tothe previously formed patterns and slowly the conductors, insulators andother regions are built up to form the final device.

The flowchart and block diagrams in the Figures illustrate possibleimplementations of fabrication and/or operation methods according tovarious embodiments of the present invention. Variousfunctions/operations of the method are represented in the flow diagramby blocks. In some alternative implementations, the functions noted inthe blocks can occur out of the order noted in the Figures. For example,two blocks shown in succession can, in fact, be executed substantiallyconcurrently, or the blocks can sometimes be executed in the reverseorder, depending upon the functionality involved.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdescribed herein.

1. A superconducting device comprising: a first mixing device having afirst mixing port and a second mixing port; and a second mixing devicehaving another first mixing port and another second mixing port, thefirst and second mixing devices being superconducting nondegeneratethree-wave mixing devices, wherein the first mixing port and the anotherfirst mixing port are configured to couple to a first coupler, whereinthe second mixing port and the another second mixing port are configuredto couple to a second coupler; wherein the first mixing port, theanother first mixing port the second mixing port, and the another secondmixing port are bidirectional; wherein the first and second couplers arebidirectional.
 2. The superconducting device of claim 1, wherein thefirst mixing device and the second mixing device are coupled inparallel.
 3. The superconducting device of claim 1, wherein the firstmixing port of the first mixing device and the another first mixing portof the second mixing device are configured to have a firstfunctionality.
 4. The superconducting device of claim 3, wherein thesecond mixing port of the first mixing device and the another secondmixing port of the second mixing device are configured to have a secondfunctionality.
 5. The superconducting device of claim 4, wherein thefirst mixing device has a third mixing port and the second mixing devicehas another third mixing port.
 6. The superconducting device of claim 5,wherein the third mixing port of the first mixing device and the anotherthird mixing port of the second mixing device are configured to have athird functionality.
 7. The superconducting device of claim 1, whereinthe first mixing device and the second mixing device are configured toreceive a signal from the first coupler.
 8. The superconducting deviceof claim 7, wherein the first mixing device and the second mixing deviceare configured to output the signal to the second coupler, the signalhaving been converted by the first mixing device and the second mixingdevice such that the second coupler is configured to output the signalvia one port.
 9. The superconducting device of claim 1, wherein thefirst mixing device and the second mixing device are configured toreceive a signal from the second coupler.
 10. The superconducting deviceof claim 9, wherein the first mixing device and the second mixing deviceare configured to output the signal to the first coupler, the signalhaving been converted by the first mixing device and the second mixingdevice such that the first coupler is configured to output the signalvia one port.
 11. The superconducting device of claim 1, wherein: thefirst coupler and the second coupler are 90 degree hybrid couplers; thefirst coupler is a 90 degree hybrid coupler and the second coupler is a180 degree hybrid coupler; or the first coupler is a 180 degree hybridcoupler and the second coupler is a 90 degree hybrid coupler. 12-22.(canceled)
 23. A superconducting four-port circulator comprising: afirst Josephson parametric device having a first signal port and asecond idler port; and a second Josephson parametric device havinganother first signal port and another second idler port, the first andsecond mixing devices being superconducting nondegenerate three-wavemixing devices, wherein the first signal port and the another firstsignal port are configured to couple to a first coupler, wherein thesecond idler port and the another second idler port are configured tocouple to a second coupler; wherein the first signal port, the anotherfirst signal port, the second idler port, and the another second idlerport are bidirectional. 24-25. (canceled)